发表机构
The Francis Crick Institute; University College London; London Centre for Nanotechnology; University of Oxford（弗朗西斯·克里克研究所; 伦敦大学学院; 伦敦纳米技术中心; 牛津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过建模与数值方法，揭示空间异质性引起的扩散延迟可在激活-抑制系统中引发时空振荡，并确定临界长度对应Hopf分岔，为理解生物振荡提供新途径。
AI 中文摘要
时间振荡在具有反馈回路或显式延迟的生物系统中自然产生。当纳入空间效应时，传播信号的旅行时间也能产生内在延迟，而在存在空间异质性的情况下，这种行为会进一步复杂化。在本工作中，我们通过数学建模、模拟和数值方法的组合，研究了一个具有空间异质性的代表性激活-抑制系统中由内在扩散延迟驱动的时空振荡的机制起源和动力学。与延迟微分方程模型中延迟被显式规定不同，在我们考虑的偏微分方程系统中，延迟是信号在空间中传播时间的固有结果。我们证明，当系统尺寸通过一个临界长度增大时，空间异质反馈可以导致无阻尼振荡的产生。在这个临界长度上，系统达到稳态的时间发散，并且系统首次出现具有正实部和非零虚部的特征值，对应于Hopf分岔。我们推断，这个临界长度可以定义系统尺寸的理论上限，超过该上限振荡会阻碍功能。本工作建立的分析流程为理解由扩散物种介导相互作用的多种生物系统中时空振荡和Hopf分岔的发生提供了一条新途径。
英文摘要
Temporal oscillations arise naturally in biological systems with feedback loops or explicit delays. When incorporating spatial effects, the travel times of propagating signals can also generate intrinsic delays, and this behaviour is complicated further in the presence of spatial heterogeneity. In this work, we investigate the mechanistic origin and dynamics of spatiotemporal oscillations driven by intrinsic diffusive delays in a representative activator-inhibitor system with spatial heterogeneity using a combination of mathematical modelling, simulations and numerical methods. In contrast to delay-differential equation models where delays are explicitly prescribed, in the partial differential equation system we consider here delays are an intrinsic consequence of signal travel time through space. We demonstrate that undamped oscillations can arise as a result of spatially heterogeneous feedback when the system size increases through a critical length. At this critical length the time for systems to reach steady-state diverges, and the systems first exhibit an eigenvalue with a positive real part and non-zero imaginary part, corresponding to a Hopf bifurcation. We infer that this critical length could define a theoretical upper limit for the size of systems where oscillations hinder function. The analysis pipeline derived in this work offers a novel route for understanding the onset of spatiotemporal oscillations and Hopf bifurcations in a diverse array of biological systems where interactions are mediated by diffusive species.
Comments26 pages, 5 figures
